What is the derivative of (5x^3-7^8) ?

The derivative of (5x^3-7^8) is 120x^2(5x^3-7)^7

What is the first derivative of (5x^3-7^8) ?

The first derivative of (5x^3-7^8) is 120x^2(5x^3-7)^7

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\frac{d}{d x} ((5 x^{3} - 7)^{8})

120 x^{2} (5 x^{3} - 7)^{7}

Solution steps

\frac{d}{d x} ((5 x^{3} - 7)^{8})

Apply the chain rule:

8 (5 x^{3} - 7)^{7} \frac{d}{d x} (5 x^{3} - 7)

= 8 (5 x^{3} - 7)^{7} \frac{d}{d x} (5 x^{3} - 7)

\frac{d}{d x} (5 x^{3} - 7) = 15 x^{2}

= 8 (5 x^{3} - 7)^{7} \cdot 15 x^{2}

Simplify

= 120 x^{2} (5 x^{3} - 7)^{7}

What is the derivative of (5x^3-7^8) ?
The derivative of (5x^3-7^8) is 120x^2(5x^3-7)^7
What is the first derivative of (5x^3-7^8) ?
The first derivative of (5x^3-7^8) is 120x^2(5x^3-7)^7